Nuclear Spin-Lattice and Spin-Spin Relaxation in hcpD2

The recovery from saturation of the $I=1\mathrm{}$ and $I=2\mathrm{}$ nuclear spin systems for hcp ${\mathrm{D}}_2$ with para deuterium mole fractions of 0.33 and 0.51 has been studied for temperatures below 5 K. Also, new values of the second moment of the $I=1\mathrm{}$ absorption line shape below 8 K are presented. Two experimental techniques were used. The first was the conventional one where the total line was saturated by a radio-frequency pulse at the Larmor frequency. For the second one, only the central section in the line was saturated ("hole-burning experiment"). The recovery of the $I=1\mathrm{}$ system after saturation could be decomposed into two parts characterized by a long and a short relaxation time, ${\tau }_l$ and ${\tau }_s$, respectively. The $I=2\mathrm{}$ system recovered with a single characteristic time, equal to ${\tau }_l$. An analysis of the spin relaxation times in terms of a three-energy-bath model is presented. It relates the observed ${\tau }_l$ and ${\tau }_s$ to the intrinsic spin-lattice relaxation times ${\tau }_{11}$ and ${\tau }_{22}$ for the $I=1\mathrm{}$ and $I=2\mathrm{}$ systems, respectively, and to the cross-relaxation time ${\tau }_{12}$ between these spin systems. The rate ${\tau }_{22}^{-1\mathrm{}}$ is small compared with ${\tau }_{11}^{-1\mathrm{}}$ and ${\tau }_{12}^{-1\mathrm{}}$ and consequently its magnitude could only be estimated very roughly from the data. The result is not inconsistent with a calculation by Harris based on an induced polarization of the $J=0\mathrm{}$ molecules. The cross-relaxation time ${\tau }_{12}$ is believed to be governed by the rate of energy diffusion through the NMR line and has been compared with an extension of the treatment by Bloembergen et al. for inhomogeneously broadened lines. Order-of-magnitude agreement is found over the temperature range investigated. The conclusions of this study remove several apparent anomalies which arose in previous less detailed NMR work on solid ${\mathrm{D}}_2$. In particular, using the mechanism of cross-relaxation just mentioned, we have reinterpreted the relaxation measurements of Smith et al. in the rotationally ordered (cubic) phase of ${\mathrm{D}}_2$.